Such pressing devices and methods for pressing have already become known in various aspects. For example, reference is made to WO 03/049883 A1 (U.S. Pat. No. 7,779,523 B2). The known pressing devices or the known methods for pressing appear to be improvable with regard to press-joining compression parts with different diameters with respect to subsequent pressing operations. Such a known pressing device and such a known method are designed to compress, with one configuration of the pressing device, a multiplicity of compression parts having the same dimensions with respect to the chain-like pressing device. Some pressing members of the known pressing device are acted on by other pressing members of the known pressing device by means of interacting surfaces following a circular shape in plan view. In the case of inner pressing members with a relatively large size in the circumferential direction, this configuration still allows an advantageous interaction. However, said configuration can be insufficient in the case of inner pressing members which are smaller in the circumferential direction.